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math.NA2015★ 1 cited
Symplectic integrators for the matrix Hill's equation and its applications to engineering models
Philipp Bader, Sergio Blanes, Enrique Ponsoda +1
We consider the numerical integration of the matrix Hill's equation. Parametric resonances can appear and this property is of great interest in many different physical applications…
math.NA2015
Volume Preservation by Runge-Kutta Methods
Philipp Bader, David I McLaren, G. R. W. Quispel +1
It is a classical theorem of Liouville that Hamiltonian systems preserve volume in phase space. Any symplectic Runge-Kutta method will respect this property for such systems, but i…